A Simulation Based Specification Test for Diffusion Processes

32 Pages Posted: 4 Oct 2005 Last revised: 11 Sep 2008

See all articles by Geetesh Bhardwaj

Geetesh Bhardwaj

SummerHaven Investment Management

Valentina Corradi

Queen Mary, University of London

Norman R. Swanson

Rutgers University - Department of Economics; Rutgers, The State University of New Jersey - Department of Economics

Date Written: 2008

Abstract

This paper makes two contributions. First, we outline a simple simulation based framework for constructing conditional distributions for multi-factor and multi-dimensional diffusion processes, for the case where the functional form of the conditional density is unknown. The distributions can be used, for example, to form predictive confidence intervals for time period t Tau , given information up to period t. Second, we use the simulation based approach to construct a test for the correct specification of a diffusion process. The suggested test is in the spirit of the conditional Kolmogorov test of Andrews (1997). However, in the present context the null conditional distribution is unknown and is replaced by its simulated counterpart. The limiting distribution of the test statistic is not nuisance parameter free. In light of this, symptotically valid critical values are obtained via appropriate use of the block bootstrap. The suggested test has power against a larger class of alternatives than tests that are constructed using marginal distributions/densities, such as those in Ait-Sahalia (1996) and Corradi and Swanson (2005a). The findings of a small Monte Carlo experiment underscore the good finite sample properties of the proposed test, and an empirical illustration underscores the ease with which the proposed simulation and testing methodology can be applied.

Keywords: Block bootstrap, diffusion processes, parameter estimation error, simulated GMM, stochastic volatility

JEL Classification: C22, C51

Suggested Citation

Bhardwaj, Geetesh and Corradi, Valentina and Swanson, Norman Rasmus and Swanson, Norman Rasmus, A Simulation Based Specification Test for Diffusion Processes (2008). Journal of Business and Economic Statistics, Vol. 26, No. 2, pp. 176-193, Available at SSRN: https://ssrn.com/abstract=812087

Geetesh Bhardwaj

SummerHaven Investment Management ( email )

Soundview Plaza,
1266 East Main Street
Stamford, CT 06902
United States

Valentina Corradi

Queen Mary, University of London ( email )

Mile End Road
London, London E1 4NS
United Kingdom

Norman Rasmus Swanson (Contact Author)

Rutgers University - Department of Economics ( email )

NJ
United States

HOME PAGE: http://econweb.rutgers.edu/nswanson/

Rutgers, The State University of New Jersey - Department of Economics ( email )

75 Hamilton Street
New Brunswick, NJ 08901
United States
848-932-7432 (Phone)

HOME PAGE: http://econweb.rutgers.edu/nswanson/

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